Multiphysics Modeling of Gas Plasma-Based Wound Healing Process Y. Sakiyama1, M. Orazov1, D. B. Graves1, and G. E. Morfill2 1 Department of Chemical and Biomolecular Engineering, University of California, Berkeley, USA 2 Max Planck Institute for Extraterrestrial Physics, Garching, Germany contact:
[email protected] and
[email protected]
BACKGROUND
Two Different Bactericidal Effects short-term[5] long-term[4]
Wound healing is one of the promising applications of atmospheric pressure gas plasmas in medicine. Recent clinical studies show a significant reduction of bacterial load in treated wounds without any side-effects. [1]. Plasma-generated reactive oxygen/nitrogen species (RONS) are thought to be directly or indirectly responsible for the bacterial elimination. Previous experimental results suggest that those reactive species have both instantaneous and long-term bactericidal effect. [2-5] In order to investigate the short- and long-term antimicrobial effect on wound healing, we adapted a five species mechano-chemical model of epithelial wound healing. [6] Our preliminary simulation result [7] shows that the prolonged effect of plasmas is important and that the initial reduction in the bacterial population may not be sufficient for improved healing.
MODEL DESCRIPTION Governing Equations • 6-species PDEs
plasma-generated RONS
• Oxygen: c
• 1-D Cartesian coordinates
healed tissue
wounded tissue
• modified parameters • additional terms for plasma treatment
k1 c c ( Dc c) k4bc k5b Pn k2 e t 1 kb e k3 c
k8 H (c cL ) H (cH c ) a ( Da a ) k6 ab k7 a t 1 e
• Capillary tips: n
• Blood vessels: b
oxygen
n en b a k13b(k14e k15 f b) 2 2 t (1 e )(1 a )
n en n ( Dnn) a a (k9b k10 n) n(k11n k12b) 2 2 t (1 e )(1 a )
chemotaxis
Reaction Pathways in the Model chemoattractants
production
consumption by bacteria
bacterial load
bacteria
• Chemoattractants : a
plasma treatment
capillary tips
blood vessels
fibroblasts
ECM
production by capillary tips
• Fibroblasts: f
• Extracellular matrix (ECM): e
f f k16 fc k17 f 2 f ( D f f ) a 2 t (1 a ) 1 c (1 c)(1 e)
e k18 f c(k19 c e) t deposition
chemotaxis
SIMULATION RESULTS Bactericidal Effects of Plasmas
Initial condition
RPn1 exp(k p t )
0.6 0.4
0.0 0.0
0.5
1.0
1.5 2.0 time [d]
0.4
0.5
1.0 1.5 2.0 time [week]
2.0 1.5 1.0 0.5
3.0
chemoattractants oxygen capillary tips blood vessels fibroblasts ECM
Plasma-treated
2.5
2.5
0.5 0.5
1.0 position [cm]
2.0 1.5
1.5
2.0
Contribution of long/short-term effect chemoattractants oxygen capillary tips blood vessels fibroblasts ECM
0.0 3.0
plasma-treated
1.0
3.0
Untreated
[-] 0.0 0.0
2.5
[-] normalized variables
0.6
normalized variables
fraction of wounded tissue
untreated
1.5
chemoattractants oxygen capillary tips blood vessels fibroblasts ECM
healed tissue
wounded tissue
Chronic Wound Healing After 3 weeks 2.5
0.8
2.0
0.0 0.0
3.0
1.0
0.2
2.5
0.2
1 RPn1{exp(k p t ) 1}
Fraction of wounded tissue
short-term
long-term
(fast healing) 1
4
Initial log reduction
Fraction of bacterial load: Pn
0.8 Pn [-]
Twice/day plasma treatment • Short-term effect: 99% direct reduction (R) • Long-term effect: 90 min doubling time (kp)
normalized variables
1.0
[-]
3.0
3.5
0.8
3 2.5
0.6
2
0.4
1.5 0.2 1
1.0 0.5 0.0 0.0
0.5
1.0 position [cm]
1.5
2.0
99% reduction + 90 min doubling
CONCLUDING REMARKS We developed a 6-species mechano-chemical wound healing model with plasma sterilization effects. In our model, the reduction of bacterial load increases oxygen concentration in wound and promote the healing process. We proposed that gas plasma treatment of wound has two effects: the initial reduction of bacterial load (short-term effect) and the delay of bacterial growth rate (long-term effect). The present results suggest several important directions for coupling plasma models with models of tissue biochemical responses.
40
60
80
100
120
140
0
Doubling time of bacteria [min] (slow healing)
REFERENCES [1] G. Isbary, et al., Br J Dermatol. 163 (2010) 78 [2] G. Morfill, et al., New J. Phys. 11 (2009) 115019 [3] M. Traylor, et al., J. Phys. D 44 (2011) 472001 [4] T. Nosenko, et al., New J. Phys. 11 (2009) 115013 [5] M. Pavlovich, et al., Plasma Process. Polym. (submitted) [6] J. A. Flegg, et al., Bull. Math. Biol. 72 (2010) 1867 [7] M. Orazov, et al., J. Phys. D (submitted)
